"We will not be intimidated," Obama said shortly after U.S. intelligence experts said the videotaped beheading of Steven Sotloff appeared to be authentic - the second such killing of an American journalist at the hands of the Islamic State.
"Their horrific acts only unite us as a country and stiffen our resolve to take the fight against these terrorists," he said. "And those who make the mistake of harming Americans will learn that we will not forget and that our reach is long and that justice will be served."
The denunciations from Obama and other U.S. officials came as details emerged about Sotloff's Israeli connections. It was unclear, however, whether such information was known previously by his captors.
In Jerusalem, a tweet by Israeli Foreign Ministry spokesman Paul Hirschson said Sotloff also had Israeli citizenship but gave no other details about his connections to the country. Sotloff "was Israeli citizen RIP," Hirschson wrote on his personal Twitter account.
There was no immediate comment from Israeli officials, but Israeli news media - regulated by censors - reported that Sotloff immigrated to Israel in 2005 . He studied at a foreign relations institute and contributed reports, including stories from the Arab world, to outlets such as the Jerusalem Post.
Obama's tougher tone stood in contrast to last week when he struggled to define U.S. strategy against the Islamic State.
The president said the U.S. objective was to destroy the group that killed Sotloff and fellow U.S. journalist James Foley "so it is no longer a threat not just to Iraq, but to the region and the United States."
He acknowledged that dismantling the group could be a prolonged effort because of the Islamic State's ability to funnel supplies and fighters over the Syrian border and because its fighters are "battle hardened" by the long insurgency in Iraq.
"This is not going to be a one-week or one-month or six-month proposition," Obama said.
The Islamic State holds strategic hubs - including Mosul, the largest city in northern Iraq - and appears to have a formidable arsenal after overrunning Iraqi military bases and other sites.
But Obama suggested that the Islamic State's "sphere of influence" could be eroded with greater international cooperation to dry up its financing and military pipelines. He gave no further details, yet such a move would probably require greater clampdowns from Western allies in the Persian Gulf and elsewhere to monitor the flow of funds and recruits to Islamic State-held territory.
At the news conference, Obama spoke directly about Sotloff and his family, saying the journalist was "taken from us in a horrific act of violence."
"We cannot even begin to imagine the agony that everyone who loves Steven is feeling right now, especially his mother, his father and his younger sister. So today our country grieves with them," Obama said. He offered similar condolences after the beheading of Foley late last month.
Oren Kessler, a Middle East research fellow at the Henry Jackson Society think tank in London and a former correspondent for The Jerusalem Post, said he and Sotloff would often discuss the challenges of being a Jewish journalist covering the Arab world.
"I would ask Steven how he felt about being a Jew, and one with connections to Israel, traveling in such dangerous places in the Arab and Muslim worlds," Kessler said.
Sotloff's response was that he was aware of the perils but believed he could reduce them to a "minor, manageable risk," Kessler said.
"I don't think Sotloff was naive. I think he was a passionate journalist who decided to brave the risks involved for the sake of his profession," Kessler said.
Michael Sapir met Sotloff when they played on a rugby team in Ra'anana, in central Israel.
"He had no real journalistic background," Sapir said. "He told me he was interested in what was happening from a world perspective. He started to write about it, and then his work started to take on a more professional journalistic tone."
The growing crisis with the Islamic State took center stage in Estonia despite the other critical message Obama carried to the small Baltic states: reassurance to the former Soviet republics that the United States and NATO stand ready to defend them against possible Russian aggression.The meeting came ahead of a NATO summit in Wales that is expected to be dominated by the showdowns in Ukraine between pro-Moscow rebels and the Western-leaning government in Kiev.
Obama arrived in this walled medieval capital on the Baltic Sea as Ukrainian President Petro Poroshenko announced an agreement with Russian President Vladimir Putin on a cease-fire "process" in eastern Ukraine, a surprise decision that came as Russian-backed rebels have made rapid strides to retake territory in the past week.
Putin later said that he and Poroshenko had agreed to the framework of a plan to end the conflict. Putin outlined a seven-point proposal that appeared to entrench the rebels' territorial gains by requiring a large-scale Ukrainian military pullback and the presence of international observers to enforce a cease-fire.
Washington Post staff writers Anne Gearan and Michelle Boorstein in Washington and Ruth Eglash in Jerusalem contributed to this report.